Quantum Gravity Theory Founded on Device That Generates Energy from Relative Acceleration Amongst Charged Particles Electrostatically Interacting Under Curvature Deviation

This is an introduction to a new concept of quantum gravity that seamlessly merges General Relativity to the Standard Model. Based upon a novel patent-pending magnetic confinement method that was designed to emulate how our sun confines and rotates charged particles about a singularity; this confinement method uses a collective of off-centered confinement coils that are directed to curve rotating charged particles about a singularity in a way that allows charged particles to relatively accelerate from geodesic deviation. With this confinement method, the subtle Relative Accelerated Energy (RAE) from deviating charged particles has the capability to be focused and exponentially increased relative to the mass-energy of a closed system; which allows for a simple pathway to understand how black holes operate at their singularities. While in the pursuit of proving that this novel method of confinement mimics how our sun operates; I was also able to develop a logical explanation of how our sun reverses its magnetic poles and cycles using the core principles of Michael Faraday. If this concept of quantum gravity is correct, there is a simple explanation for the additional observed gravitational force about the galaxies that are said to obtain dark matter. In short, this theory of quantum gravity has the potential to fully discredit the existence of theorized dark matter with a simple experiment.

Quantum Gravity Theory Founded on Device That Generates Energy from Relative Acceleration Amongst Charged Particles Electrostatically Interacting Under Curvature Deviation

This is an introduction to a new concept of quantum gravity that seamlessly merges General Relativity to the Standard Model. Based upon a novel patent-pending magnetic confinement method that was designed to emulate how our sun confines and rotates charged particles about a singularity; this confinement method uses a collective of off-centered confinement coils that are directed to curve rotating charged particles about a singularity in a way that allows charged particles to relatively accelerate from geodesic deviation. With this confinement method, the subtle Relative Accelerated Energy (RAE) from deviating charged particles has the capability to be focused and exponentially increased relative to the mass-energy of a closed system; which allows for a simple pathway to understand how black holes operate at their singularities. While in the pursuit of proving that this novel method of confinement mimics how our sun operates; I was also able to develop a logical explanation of how our sun reverses its magnetic poles and cycles using the core principles of Michael Faraday. If this concept of quantum gravity is correct, there is a simple explanation for the additional observed gravitational force about the galaxies that are said to obtain dark matter. In short, this theory of quantum gravity has the potential to fully discredit the existence of theorized dark matter with a simple experiment.

Groundbreaking Testable Quantum Theory of Gravity That Provides the Essential Components Needed in Calculating the Energy of Black holes at Singularities

This is an introduction to a new concept of quantum gravity that seamlessly merges General Relativity to the Standard Model. Based upon a novel patent-pending magnetic confinement method that was designed to emulate how our sun confines and rotates charged particles about a singularity; this confinement method uses a collective of off-centered confinement coils that are directed to curve rotating charged particles about a singularity in a way that allows charged particles to relatively accelerate from geodesic deviation. With this confinement method, the subtle Relative Accelerated Energy (RAE) from deviating charged particles has the capability to be focused and exponentially increased relative to the mass-energy of a closed system; which allows for a simple pathway to understand how black holes operate at their singularities. While in the pursuit of proving that this novel method of confinement mimics how our sun operates; I was also able to develop a logical explanation of how our sun reverses its magnetic poles and cycles using the core principles of Michael Faraday. If this concept of quantum gravity is correct, there is a simple explanation for the additional observed gravitational force about the galaxies that are said to obtain dark matter. In short, this theory of quantum gravity has the potential to fully discredit the existence of theorized dark matter with a simple experiment.

Curvature

The mathematics of Riemannian curvature is presented. The Riemann curvature tensor and its role in parallel transport, in the metric, and in geodesic deviation are expounded at length. We begin by defining the curvature tensor and the torsion tensor by relating them to covariant derivatives. Then the local metric is obtained up to second order in terms of Minkowski metric and curvature tensor. Geometric issues such as the closure or non-closure of parallelograms are discussed. Next, the relation between curvature and parallel transport around a loop is derived. Then we proceed to geodesic deviation. The influence of global properties of the manifold on parallel transport is briefly expounded. The Lie derivative is then defined, and isometries of spacetime are discussed. Killing’s equation and properties of Killing vectors are obtained. Finally, the Weyl tensor (conformal tensor) is introduced.

Geodesic Uncertainty in Diffusion MRI

We study theoretical and operational issues of geodesic tractography, a geometric methodology for retrieving biologically plausible neural fibers in the brain from diffusion weighted magnetic resonance imaging. The premise is that true positives are geodesics in a suitably constructed metric space, but unlike traditional first order methods these are not a priori constrained to connect nongeneric points on subdimensional manifolds, such as the characteristics in traditional streamline methods. By virtue of the Hopf-Rinow theorem geodesic tractography furnishes a huge amount of redundancy, ensuring the a priori existence of at least one tentative fiber between any two points and permitting additional tractometric and data-extrinsic constraints for (fuzzy or crisp) classification of true and false positives. In our feasibility study we consider a hybrid paradigm that unifies existing ideas on tractography, combining deterministic and probabilistic elements in a way naturally supported by metric geometry. Particular attention is paid to an analytical prediction of geodesic deviation on numerically computed geodesics, a ‘tidal’ effect induced by small perturbations resulting from data noise. Taking these effects into account clarifies the inherent uncertainty of geodesics, while simultaneosuly offering a dimensionality reduction of the tractography problem.

Tidal forces in Kottler spacetimes

The article considers tidal forces in the vicinity of the Kottler black hole. We find a solution of the geodesic deviation equation for radially falling bodies, which is determined by elliptic integrals. And also the asymptotic behavior of all spatial geodesic deviation vector components were found. We demonstrate that the radial component of the tidal force changes sign outside the single event horizon for any negative values of the cosmological constant, in contrast to the Schwarzschild black hole, where all the components of the tidal force are sign-constant. We also find the similarity between the Kottler black hole and the Reissner–Nordström black hole, because we indicate the value of the cosmological constant, which ensures the existence of two horizons of the black hole, between which the angular components of the tidal force change sign. It was possible to detect non-analytical behavior of geodesic deviation vector components in anti-de Sitter spacetime and to describe it locally.

Tidal effects in 4D Einstein–Gauss–Bonnet black hole spacetime

We have investigated tidal forces and geodesic deviation motion in the 4D-Einstein–Gauss–Bonnet spacetime. Our results show that tidal force and geodesic deviation motion depend sharply on the sign of Gauss–Bonnet coupling constant. Comparing with Schwarzschild spacetime, the strength of tidal force becomes stronger for the negative Gauss–Bonnet coupling constant, but is weaker for the positive one. Moreover, tidal force behaves like those in the Schwarzschild spacetime as the coupling constant is negative, and like those in Reissner–Nordström black hole as the constant is positive. We also present the change of geodesic deviation vector with Gauss–Bonnet coupling constant under two kinds of initial conditions.

Raychaudhuri Equation, Geometrical Flows and Geometrical Entropy

The Raychaudhuri equation is derived by assuming geometric flow in space–time M of n+1 dimensions. The equation turns into a harmonic oscillator form under suitable transformations. Thereby, a relation between geometrical entropy and mean geodesic deviation is established. This has a connection to chaos theory where the trajectories diverge exponentially. We discuss its application to cosmology and black holes. Thus, we establish a connection between chaos theory and general relativity.